Open AccessMean‐field formulation for the infinite‐horizon mean–variance control of discrete‐time linear systems with multiplicative noises
Author(s) -
Barbieri Fabio,
Costa Oswaldo L. V.
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2020.0442
Subject(s) - mathematics , multiplicative function , multiplicative noise , optimal control , mathematical optimization , stochastic control , portfolio , time horizon , variance (accounting) , discrete time and continuous time , control theory (sociology) , control (management) , computer science , statistics , economics , finance , mathematical analysis , signal transfer function , digital signal processing , artificial intelligence , analog signal , computer hardware , accounting
This study considers theinfinite‐horizon stochastic optimal control of a discounted and long‐run average costs under a mean–variance trade‐off performance criterion for discrete‐time linear systems subject to multiplicative noises. The authors adopt a mean‐field approach to tackle the problem and get an optimal control solution in terms of a set of two generalised coupled algebraic Riccati equations (GCAREs). Then, they establish sufficient conditions for the existence of the maximal solution and necessary and sufficient conditions for the existence of the mean‐square stabilising solution to the GCARE. From this solution, they derive optimal control policies to the related discounted and long‐run average cost problems. A numerical example illustrates the obtained results for the multi‐period portfolio selection problem in which it is desired to minimise the sum of the mean–variance trade‐off costs of a portfolio against a benchmark along the time.